Question: $\dfrac{1}{6} \div \dfrac{5}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{5}{9}$ is $\dfrac{9}{5}$ Therefore: $ \dfrac{1}{6} \div \dfrac{5}{9} = \dfrac{1}{6} \times \dfrac{9}{5} $ $ \phantom{\dfrac{1}{6} \times \dfrac{9}{5}} = \dfrac{1 \times 9}{6 \times 5} $ $ \phantom{\dfrac{1}{6} \times \dfrac{9}{5}} = \dfrac{9}{30} $